| Easy : for the curious |  |
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| Sundial of Saint Rémy de Provence Source : Wikipedia Commons |
« Put your hand on a stove for a minute and it will feel like an hour. Sit with a pretty girl for an hour and it will fly like a minute. That's relativity. »
This famous quote, attributed to Einstein 1 is a good description of the psychological side of time. Time is undeniably linked to our senses, we perceive it through duration, order and simultaneity. What will be left of it if we take those away ?
The physicist and/or mathematician is used to depicting time rather than asking himself about its nature. For him, time is more of a variable, it's the degree of freedom of bodies that interact or move in space. Concretely, this parameter permits us to measure durations (chronometry), and mark order (chronology). We can mathematically define these properties : duration is the locus in a one-dimensional space, order is represented by the orientation of this straight line.
We will see that this mathematical representation of time as a supplementary dimension of space is not characteristic of relativity theory, and Galilean kinematics can use it as well. We will then see clearly the fundamental differences between the concept of time in the two theories and we will try to understand the geometry behind the notorious change of sign of the mathematician's "ds²". We will also see that during the evolution of physical science, time has progressively lost what we thought were fundamental properties of his...
